Question

Consider the relationship between Burger Queen and a franchisee. BQ is entitled to 30% of the revenue earned by the restaurant. Weekly demand for Sloppers at the franchisee's restaurant is given by Q=4,000 - 400P. The franchisee's marginal cost per Slopper is $0.35. Assuming zero fixed cost. The restaurant's total profit = R - C. The franchisee's profit = 70% R - C. Refer to Scenario 1.1. If BQ sets the price and weekly sales quantity of Sloppers, how much does BQ receive?

a. $3,000. b. $300. c. $4,500. d. $900.

Answer 1

BQ will want to maximize the revenue, which is 0.3R, which is the same thing as maximizing R. Hence, it will choose an output where MR = 0

Now,

Q = 4000 - 400P

—> P = 10 - Q/400

TR = P x Q

—> TR = (10 - Q/400) x (4000 - 400P) = 10Q - ^{​​​​​​}Q²/400

MR is the first derivative of TR. Hence, MR = 10 - Q/200

But MR should be equal to 0 because profit maximizing quantity and price can be determined when MR = 0.

MR = 10 - Q/200 = 0

—> Q = 2000

Price can now be determined,

P = 10 - Q/400 = 10 - 2000/400 = $ 5

TR = $(5 x 2000) = $ 10000

Thus BQ will recieve 30% of $10000 = $3000

Answer = a. $3000​​​​​​​​​​​​​​​​​